On stable type IIA de-Sitter vacua with geometric flux

We present a class of tachyon-free (stable) AdS as well as dS solutions in the context of type IIA orientifold compactifications. This model is based on a type IIA setting having geometric flux which, in addition, also includes the usual NS–NS three-form flux H 3 and the RR p -form fluxes F p for p ∈ { 0 , 2 , 4 , 6 } . Although all the saxionic moduli are stabilized, there remains a combination of the RR axions which is flat, and the dS solution is realized through the D -term effects induced by the geometric fluxes, without which one can only have AdS solutions. Using flux scaling arguments we also discuss how to engineer a parametric control in these models, in the sense of realizing the respective AdS/dS solutions in large volume, weak string-coupling as well as large complex-structure regime. We also discuss open possibilities (e.g. about the unknown status on having the complete set of Bianchi identities) under which such tachyon-free dS solutions may or may not be viable.